Simplify the following expression: $ n = \dfrac{9}{4} + \dfrac{5r + 7}{r - 5} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{r - 5}{r - 5}$ $ \dfrac{9}{4} \times \dfrac{r - 5}{r - 5} = \dfrac{9r - 45}{4r - 20} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{5r + 7}{r - 5} \times \dfrac{4}{4} = \dfrac{20r + 28}{4r - 20} $ Therefore $ n = \dfrac{9r - 45}{4r - 20} + \dfrac{20r + 28}{4r - 20} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{9r - 45 + 20r + 28}{4r - 20} $ $n = \dfrac{29r - 17}{4r - 20}$